Mr Trump also named Gina Haspel to become the CIA’s first female director.

How did Tillerson react?

Speaking to reporters at the Department of State, Mr Tillerson said good work had been done to have better relations with China, and rein in North Korea’s nuclear weapons programme.

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Media captionFrom “moron” to “castration”: a history of Trump v Tillerson bust-ups

But he added: “Much work remains to respond to the troubling behaviour and actions on the part of the Russian government.

“Russia must assess carefully as to how its actions are in the best interest of the Russian people and of the world more broadly. Continuing on their current trajectory is likely to lead to greater isolation on their part, a situation which is not in anyone’s interest.”

Sounding breathless and looking shaken, Mr Tillerson said he had spoken to the president to ensure clarity in the days ahead.

Although Mr Tillerson will not officially leave until 31 March, his deputy John Sullivan take over running the state department pending the confirmation of Mr Pompeo.

“What is most important is to ensure an orderly and smooth transition during a time that the country continues to face significant policy and national security challenges,” Mr Tillerson said.

What was Trump’s reason?

Skip Twitter post by @realDonaldTrump

Mike Pompeo, Director of the CIA, will become our new Secretary of State. He will do a fantastic job! Thank you to Rex Tillerson for his service! Gina Haspel will become the new Director of the CIA, and the first woman so chosen. Congratulations to all!

— Donald J. Trump (@realDonaldTrump) March 13, 2018

End of Twitter post by @realDonaldTrump

Speaking to reporters outside the White House on Tuesday, Mr Trump said his differences with Mr Tillerson came down to personal “chemistry”.

“We got along actually quite well, but we disagreed on things,” said the president.

“When you look at the Iran deal, I think it’s terrible. I guess he thought it was OK.

“With Mike, Mike Pompeo, we have a very similar thought process. I think it’s going to go very well.”

Mr Tillerson is the latest in a long list of senior officials who have either resigned or been fired since Mr Trump took office.

The White House revolving door: Who’s gone?

‘You’re fired!’ – A reality TV White House?

How was Tillerson fired?

The White House and Mr Tillerson have had a series of public disagreements – and that continued until the very end.

Both sides have offered a different accounts of when the Secretary of State was told he was being fired.

The White House insists Mr Tillerson received a phone call on Friday from Chief of Staff John Kelly, who told him that he was being let go.

They say Mr Tillerson then asked if the announcement could be held until his return from a tour of Africa.

The top US diplomat’s team said he felt unwell on Saturday and decided to cut short his tour by a day.

His firing was reported by the Washington Post on Tuesday before any tweet was sent, according to a White House official.

But a statement released by Under Secretary Steve Goldstein implied that Mr Tillerson was first made aware of his firing by President Trump’s tweet.

“The secretary did not speak to the president and is unaware of the reason,” he said. After this statement was released Mr Goldstein himself was fired by the White House.

Mr Tillerson also said he received a call from the president about three hours after Mr Trump sent a tweet announcing his departure.

Rex Tillerson – Trump’s former top diplomat

Reaction to his firing

The odd couple of politics no more

Analysis by Jon Sopel, BBC North America editor

The end was a perfect metaphor for the relationship. The odd couple of politics had been yoked together for too long.

Men of different temperaments, demeanour and style had reached a parting of the ways.

The secretary of state landed back at Joint Base Andrews to have a member of staff inform him that the president had tweeted.

Because Mr Tillerson is not on Twitter, the tweet had to be printed out. Fancy being the one tasked with handing that over to the boss. Fired by a tweet.

The career of a one-time giant of corporate America had come to an ignominious end.

Read Jon’s analysis in full

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Media captionMike Pompeo: Meet America’s new top diplomat

Who are the nominees?

A US Senate report found that Ms Haspel ran a CIA prison in Thailand where prisoners were waterboarded in 2002.

The CIA deputy director was also accused of destroying dozens of videotapes of interrogations at the camp.

Gina Haspel – first female CIA director nominee

Mr Pompeo is a hardline conservative former lawmaker from Kansas and a Trump loyalist.

In 2014, he defended the CIA officers who waterboarded detainees as “patriots”.

Mike Pompeo – Trump’s loyalist new diplomat

Both the new secretary of state and CIA director will have to be confirmed by the Senate.

What did Trump and Tillerson disagree on?

Reports had swirled since last year of a rift between the commander-in-chief and his top diplomat.

Last October Mr Tillerson was forced to convene a news conference to deny claims he planned to quit, though he did not address a report that he had referred to his boss as a “moron” after a Pentagon meeting.

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Media captionTrump says goodbye to Tillerson: ‘I like Rex a lot, but we disagreed’

Mr Trump also publicly undercut the former Texas oilman by tweeting that he was “wasting his time” trying to negotiate with North Korea.

In December, the secretary of state offered to begin direct talks with Pyongyang without preconditions.

Battles ahead after another sacking from Trump Cabinet

The White House – which insisted North Korea must first accept any negotiations would be about giving up its nuclear arsenal – distanced itself from his remarks.

Mr Tillerson was reported to be astonished at how little Mr Trump grasped the basics of foreign policy.